HOW POISSON DISTRIBUTION TEAM ANALYSIS SOFTWARE WORKS?
This document will describe to user the engine behind the Poisson Distribution Team Analysis Software.
Predicting correct scores of soccer matches
Using Poisson distribution it is possible to predict the probability of a certain outcome. This calculation relies upon knowing what has happened historically in the sample set of results. It should be noted that while history can be a guide it can not be certain that history will repeat itself but Poisson distribution will allow you to view the probability that the outcome will match your historical information. Lets take soccer as an example.
The calculation is :-
=(((POWER(Historic average goals scored , Number of goals required))*POWER(2.718,-Historic average goals scored))/FACT(Score required))
If for example we had a team that scored an average 1.79 goals at home and we wanted to find the probability that they would score 2 in the next match the calculation would be.
=(((POWER(1.79, 2))*POWER(2.718,-1.79))/FACT(2))
=26.75%
Taking this a step further. We know that the home team now has a 26.75% chance of scoring two goals. If the full result we wanted was a 2-1 win for the home team we can calculate this event. We know that the away team had scored an average of 1.41 goals away from home. We would calculate the away teams probability of scoring one using the above formula. This would equal 34.43%. Then all we need to do is multiply these probabilities as they are mutually exclusive / independent events. =(.2675*.3443)
Therefore there is a 9.21% chance of a 2-1 win for the home team based on our historical evidence.
=(((POWER(Historic average goals scored , Number of goals required))*POWER(2.718,-Historic average goals scored))/FACT(Score required)) |
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To complete the calculation of the total possible result with two teams multiply the equation by itself as the outcomes are mutually exclusive / independent. |
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Games home team has played at home |
17 |
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Goals home team has scored at home |
42 |
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Games away team has played away |
17 |
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Goals away team has scored away |
28 |
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Home team has scored average goals |
2.47 |
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Away team has scored average goals |
1.65 |
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P(e) |
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Home score required |
2 |
25.81% |
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Away score required |
1 |
31.73% |
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Probability of match result |
2-1 |
8.19% |
Fair odds are around 13 to one |
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Simple calculation of the probability of certain scores (This is not the full calculation but can be used as a guide) |
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Home win : |
55.49% = Sum of P(e) |
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Home Team |
Away team |
P(H) |
P(A) |
P(e) |
Fair odds |
||||
7 |
0 |
0.94% |
19.26% |
0.18% |
551 |
||||
7 |
1 |
0.94% |
31.73% |
0.30% |
335 |
||||
7 |
2 |
0.94% |
26.13% |
0.25% |
406 |
||||
7 |
3 |
0.94% |
14.35% |
0.14% |
740 |
||||
7 |
4 |
0.94% |
5.91% |
0.06% |
1796 |
||||
7 |
5 |
0.94% |
1.95% |
0.02% |
5452 |
||||
7 |
6 |
0.94% |
0.53% |
0.01% |
19861 |
||||
6 |
0 |
2.67% |
19.26% |
0.51% |
195 |
||||
6 |
1 |
2.67% |
31.73% |
0.85% |
119 |
||||
6 |
2 |
2.67% |
26.13% |
0.70% |
144 |
||||
6 |
3 |
2.67% |
14.35% |
0.38% |
261 |
||||
6 |
4 |
2.67% |
5.91% |
0.16% |
634 |
||||
6 |
5 |
2.67% |
1.95% |
0.05% |
1925 |
||||
5 |
0 |
6.49% |
19.26% |
1.25% |
81 |
||||
5 |
1 |
6.49% |
31.73% |
2.06% |
49 |
||||
5 |
2 |
6.49% |
26.13% |
1.69% |
60 |
||||
5 |
3 |
6.49% |
14.35% |
0.93% |
108 |
||||
5 |
4 |
6.49% |
5.91% |
0.38% |
261 |
||||
4 |
0 |
13.13% |
19.26% |
2.53% |
40 |
||||
4 |
1 |
13.13% |
31.73% |
4.16% |
25 |
||||
4 |
2 |
13.13% |
26.13% |
3.43% |
30 |
||||
4 |
3 |
13.13% |
14.35% |
1.88% |
54 |
||||
3 |
0 |
21.25% |
19.26% |
4.09% |
25 |
||||
3 |
1 |
21.25% |
31.73% |
6.74% |
15 |
||||
3 |
2 |
21.25% |
26.13% |
5.55% |
19 |
||||
2 |
0 |
25.81% |
19.26% |
4.97% |
21 |
||||
2 |
1 |
Prediction |
25.81% |
31.73% |
8.19% |
13 |
<-- Most likely result in this section |
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1 |
0 |
20.89% |
19.26% |
4.02% |
25 |
||||
Away win : |
25.16% = Sum of P(e) |
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Home Team |
Away team |
P(H) |
P(A) |
P(e) |
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0 |
7 |
8.46% |
0.13% |
0.01% |
9410 |
||||
1 |
7 |
20.89% |
0.13% |
0.03% |
3809 |
||||
2 |
7 |
25.81% |
0.13% |
0.03% |
3084 |
||||
3 |
7 |
21.25% |
0.13% |
0.03% |
3744 |
||||
4 |
7 |
13.13% |
0.13% |
0.02% |
6062 |
||||
5 |
7 |
6.49% |
0.13% |
0.01% |
12267 |
||||
6 |
7 |
2.67% |
0.13% |
0.00% |
29791 |
||||
0 |
6 |
8.46% |
0.53% |
0.05% |
2214 |
||||
1 |
6 |
20.89% |
0.53% |
0.11% |
897 |
||||
2 |
6 |
25.81% |
0.53% |
0.14% |
726 |
||||
3 |
6 |
21.25% |
0.53% |
0.11% |
881 |
||||
4 |
6 |
13.13% |
0.53% |
0.07% |
1427 |
||||
5 |
6 |
6.49% |
0.53% |
0.03% |
2887 |
||||
0 |
5 |
8.46% |
1.95% |
0.16% |
608 |
||||
1 |
5 |
20.89% |
1.95% |
0.41% |
246 |
||||
2 |
5 |
25.81% |
1.95% |
0.50% |
200 |
||||
3 |
5 |
21.25% |
1.95% |
0.41% |
242 |
||||
4 |
5 |
13.13% |
1.95% |
0.26% |
392 |
||||
0 |
4 |
8.46% |
5.91% |
0.50% |
201 |
||||
1 |
4 |
20.89% |
5.91% |
1.23% |
82 |
||||
2 |
4 |
25.81% |
5.91% |
1.52% |
66 |
||||
3 |
4 |
21.25% |
5.91% |
1.26% |
80 |
||||
0 |
3 |
8.46% |
14.35% |
1.21% |
83 |
||||
1 |
3 |
20.89% |
14.35% |
3.00% |
34 |
||||
2 |
3 |
25.81% |
14.35% |
3.70% |
28 |
||||
0 |
2 |
8.46% |
26.13% |
2.21% |
46 |
||||
1 |
2 |
20.89% |
26.13% |
5.46% |
19 |
<-- Most likely result in this section |
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0 |
1 |
8.46% |
31.73% |
2.68% |
38 |
||||
Draw : |
18.97% = Sum of P(e) |
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Home Team |
Away team |
P(H) |
P(A) |
P(e) |
|||||
0 |
0 |
8.46% |
19.26% |
1.63% |
62 |
||||
1 |
1 |
20.89% |
31.73% |
6.63% |
16 |
||||
2 |
2 |
25.81% |
26.13% |
6.74% |
15 |
<-- Most likely result in this section |
|||
3 |
3 |
21.25% |
14.35% |
3.05% |
33 |
||||
4 |
4 |
13.13% |
5.91% |
0.78% |
129 |
||||
5 |
5 |
6.49% |
1.95% |
0.13% |
793 |
||||
6 |
6 |
2.67% |
0.53% |
0.01% |
7010 |
||||
Any other score not mentioned above in any of the sections |
0.39% |
259 |
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An online version of this software can be found at : http://www.globetting.com/strategy/poisson_caculator.phtml